Q88.The area (in sq. units) of the part of circle x2 + y2 = 169 which is below the line 5x −y = 13 is πα 2β −652 + αβ sin−1( 1312 ) where α, β are coprime numbers. Then α + β is equal to
What This Question Tests
This problem requires calculating the area of a region bounded by a circle and a line, which involves splitting the area into a sector and a triangle, demanding strong geometric and trigonometric skills.
Concepts Tested
Formulas Used
Area of a sector = (1/2)r^2θ
Area of a triangle = (1/2)bh
Equation of circle x^2 + y^2 = r^2
Distance from origin to a line
📚 NCERT Sections This Tests
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
9.5 — A Small Bulb Is Placed At The Bottom Of A Tank Containing Water To A
Physics Class 12 · Chapter 9
9.5 A small bulb is placed at the bottom of a tank containing water to a depth of 80cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of water is 1.33. (Consider the bulb to be a point source.)
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
📋 Question Details
- Chapter
- Definite Integration & Area
- Topic
- Area under a curve and geometry
- Year
- 2024
- Shift
- 29 Jan Shift 1
- Q Number
- Q88
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 8: Application of Integrals
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